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A Key Generation Method Based on Reconfiguration Discrete Dynamical System

A technology of discrete dynamics and generation methods, applied in the field of information security, can solve problems such as difficult control of Lyapunov exponent and design of high-dimensional ultra-chaotic systems, and achieve the effect of precise control

Active Publication Date: 2021-06-01
HEILONGJIANG UNIV
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0027] Based on the above problems, a method of chaoticization of high-dimensional dynamical system and its chaotic sequence generation method is proposed, which solves the problem that the high-dimensional hyper-chaotic system is difficult to design and the Lyapunov exponent in the chaotic system is difficult to control. This method can well control all Designing all Lyapunov exponents in a chaotic system

Method used

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  • A Key Generation Method Based on Reconfiguration Discrete Dynamical System
  • A Key Generation Method Based on Reconfiguration Discrete Dynamical System
  • A Key Generation Method Based on Reconfiguration Discrete Dynamical System

Examples

Experimental program
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Effect test

Embodiment 1

[0046] Such as Figure 1-2 As shown, a chaoticization of high-dimensional dynamical system and its chaotic sequence generation method are as follows:

[0047] Suppose m-dimensional discrete dynamical system

[0048] S n+1 = AS n modc

[0049] where S n is the state vector (x 1 (n),x 2 (n),x 3 (n)...x m (n)) T , A is a constant coefficient matrix,

[0050]

[0051] Since there is no nonlinear term in the m-dimensional discrete dynamical system, the Jacobian matrix is ​​A, therefore, P=A n , let the m eigenvalues ​​of matrix A be λ 0 ,λ 1 ,...,λ m , m Lyapunov exponents in m-dimensional discrete chaos are:

[0052]

[0053]Therefore, the eigenvalues ​​of the parameter matrix A determine the Lyapunov index of the system; where the construction method of the parameter matrix A is as follows:

[0054] (1) Given the Lyapunov index value LE 1 ,LE 2 ,...LE m , and calculate the eigenvalues The diagonal matrix Λ based on eigenvalues ​​is constructed as

[00...

Embodiment 2

[0060] 1. Arbitrarily given 8 eigenvalues ​​greater than 1, such as 40, 41, 42, 43, 44, 45, 46, 47, and c is defined as 1. The rounded Lyapunov indices are 3.69, 3.71, 3.74, 3.76, 3.78, 3.81, 3.83, 3.85.

[0061] 2. A non-singular matrix q is defined as:

[0062]

[0063] Among them, element q(i,i)=2, i=1,2,3...m, and other elements are all 1. It is easy to show that q is a non-singular matrix. When m=8, q can be defined

[0064]

[0065] And the inverse matrix q after rounding -1 for

[0066]

[0067] 3. The parameter matrix is

[0068]

[0069] Refactoring Discrete Dynamical Systems.

[0070]

[0071] (4) Using the initial value of the state vector as the initial key, the chaotic sequence is generated by reconstructing the discrete dynamical system. Quantize to 1 when the output sequence is greater than 0.5, and quantize to 0 when the output sequence is less than 0.5.

Embodiment 3

[0073] Effect of the present invention can be further illustrated by the detection result of the following present embodiment:

[0074] 1. Detection method and content:

[0075] The SP800-22 random number detection standard provided by the National Institute of Standards and Technology NIST of the United States is used to detect the randomness of the chaotic sequence output by the chaotic sequence generator in Embodiment 2 of the present invention. The detection standard includes 15 detection contents, each A P value is included in the assay results generated by the assay. When the P value is greater than 0.01, it means that the test content is passed.

[0076] 2. Test results:

[0077] Referring to Example 2, make it generate 100 groups of 10,000,000 point random sequences, and use the SP800-22 random number detection standard provided by the National Institute of Standards and Technology NIST to detect, and one set of results is shown in Table 1-8:

[0078] Table 1x 1 (n...

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Abstract

The invention discloses a chaoticization of a high-dimensional dynamical system and a method for generating a chaotic sequence thereof. The method is as follows: suppose an m-dimensional discrete dynamical system, S n+1 = AS n modc, A is a constant coefficient matrix, since there is no nonlinear term in the m-dimensional discrete dynamical system, the Jacobian matrix is ​​A, therefore, P=A n , the eigenvalues ​​of the parameter matrix A determine the Lyapunov exponent of the system; given the Lyapunov exponent value LE 1 ,LE 2 ,...LE m , and calculate the eigenvalues, design an m×m dimensional non-singular matrix q; calculate the parameter matrix A=qΛq ‑1 , and brought into the original model to reconstruct the discrete dynamical system; the initial value of the state vector is used as the initial key, and the time series of the reconstructed discrete dynamical system is used to generate a random sequence; the present invention can realize precise control of the Lyapunov exponent, Periodic systems with periodic attractors and systems with fixed-point attractors are realized, and the chaotic sequences output by this method have more complex chaotic behavior.

Description

technical field [0001] The invention relates to the field of information security, in particular to a chaoticization of a high-dimensional dynamical system and a method for generating a chaotic sequence. Background technique [0002] Existing general chaos design methods mainly rely on the Chen-Lai algorithm, given the initial state x 0 , for the control system x 1 =f 0 (x 0 )+B 0 x 0 Compute its Jacobian matrix [0003] J 0 (x 0 ) = f 0 '(x 0 )+B 0 x 0 , [0004] And remember T 0 =J 0 (x 0 ). take B 0 x 0 = σ 0 I and choose the constant σ 0 >0 such that the matrix [T 0 T 0 T ] is limited and diagonally dominant. For k=0,1,2,..., consider the control system [0005] x k+1 =f k (x k )+B k x k , [0006] where B k x k = σ k I has been obtained from the previous step. Now do the following calculation: [0007] Step 1. Calculate the Jacobian matrix [0008] J k (x k ) = f k '(x k )+B k x k [0009] Remember T k =J k T k-1 . [0...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): H04L9/00
CPCH04L9/001
Inventor 丁群王传福余龙飞李孝友
Owner HEILONGJIANG UNIV
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